Question

f(1)=-5; f(2) = 7; f (3) = -6; f (n+3)=2f (n+2)-f(n+1)-3f(n). determine the first 5 terms of the sequence. can someone please help with this question :P

Answer 1

This is one is tougher to work, but we can do it.

With sequences the only values of n we generally use are the numbers 1, 2, 3, 4, .... These are the natural or counting numbers.

That being the case, if we substitute 1 for n the definitions says:

f(4) = 2*f(3) - f(2) -3f(1) =
f(5) = ?

Answer 2

ahh, i still dont seem to understand. i see what you did by subsituting 1 for n but i dont understand how to continue. the answer says that the first 5 terms are -5, 7,-6,-4,-23, if that helps :P

Answer 3

The problem gives us the first three terms as definitions. Check that out.

Then....

f(4) = 2*f(3) - f(2) -3f(1)
f(4) = (2*-6) - (7) - (3*-5)
f(4) = (-12) - (7) - (-15)
f(4) = -12 -7 + 15
f(4) = -4

f(5) = ? according to the pattern

Answer 4

oh!! 23!

Answer 5

But can you make it happen for yourself like I did with f(4)?